bijective_of_injective_endomorphism

English

Any injective endomorphism of an Artinian module is bijective.

Русский

Любой инъективный эндоморфизм артинанов modulo является биективным.

LaTeX

$$$\\text{Bijective}(f)$ if $f$ is injective on an Artinian module.$$

Lean4

/-- Any injective endomorphism of an Artinian module is bijective. -/
theorem bijective_of_injective_endomorphism (f : M →ₗ[R] M) (s : Injective f) : Bijective f :=
  ⟨s, surjective_of_injective_endomorphism f s⟩

Похожие утверждения